Majorana fermions of a two-dimensional px+ipy superconductor

To investigate Majorana fermionic excitations of a p(x)+ip(y) superconductor, the Bogoliubov-de Gennes equation is solved on a sphere for two cases: (i) a vortex-antivortex pair at opposite poles and (ii) an edge near the south pole and an antivortex at the north pole. The vortex cores support a state of two Majorana fermions, the energy of which decreases exponentially with the radius of the sphere, independently of a moderate disorder potential. The tunneling conductance of an electron into the superconductor near the position of a vortex is computed for finite temperature and is compared to the case of an s-wave superconductor. The zero-bias conductance peak of the antivortex is half that of the vortex. This effect can be used as a probe of the order-parameter symmetry and as a direct measurement of the Majorana fermion.